Abstract :
[en] The development of novel optoelectronic applications crucially depends on the detailed understanding of light--matter interaction in the candidate materials.
From a theoretical point of view, this task is especially difficult in the case of quasi--2D semiconductors, since their optical response is dominated by strongly bound excitons and many--body perturbation theory (MBPT) must be employed together with first--principles computer simulations.
The case of hexagonal boron nitride (hBN) is interesting because its large band gap and high absorption/emission efficiency make it amenable for the fabrication of UV emitting devices.
However, the specific microscopic mechanisms that govern the appearance of complex fine structures in the optical spectra of different types of hBN samples (monolayers, few--layers, bulk samples) are poorly understood, leading to discrepancies between experimental and theoretical results.
In this Thesis, we first show how the interlayer interaction in multilayers leads to a Davydov splitting of the excitonic states of single--layer hBN. We study and characterize the absorption spectra in single layer, multilayer and bulk hBN systems, focusing on the exciton symmetry and optical activity. We show that in multilayers, Davydov splitting leads to a surface localization of the lowest--lying optically active excitons.
These additional spectral features still cannot explain, by themselves, the experimentally measured optical fine structure. Therefore, we calculate exciton dispersion curves in order to search for the existence of indirect excitons with lower energy than the lowest direct exciton. We find that in bilayer hBN the nature of the optical gap (direct) changes with respect to the single--particle gap (indirect). In contrast, in bulk hBN (and thicker few--layers of hBN) both optical and quasiparticle gaps are indirect, i.e., they display a pronounced minimum in the excitonic dispersion curve between $\Gamma$ and K. %in accordance with the single--particle gap.
If the lowest exciton is indirect, as in bulk hBN, then phonon--assisted transitions become relevant for the description of the optical spectra. The reliable \textit{ab initio} description of exciton--phonon coupling in indirect absorption and emission is the main focus of this Thesis. We have tackled the problem with two approaches. In the static approach, we calculate the coupling of excitons with phonons in a supercell via a finite--displacement method. The supercell is commensurate with the $k$--point corresponding to the minimum of the exciton dispersion. In this way, we are able to reproduce the rich fine structure in the luminescence spectrum of bulk hBN in good agreement with experiment and to explain it in terms of exciton--phonon coupling.
The finite--displacement approach is supposed to work for indirect optical spectra in any material where the minimum of the exciton dispersion gives the dominant phonon--assisted contribution. Since in the absorption case this is not always true, we have employed a second, perturbative approach for the description of indirect absorption spectra which also includes dynamical effects and a microscopic treatment of the coupling. We have implemented the required many--body quantities (namely, the exciton--phonon coupling matrix elements and self--energy) in the \texttt{Yambo} many--body code. We expect this new method to allow us to overcome many of the theoretical limitations of previous approaches to indirect absorption.
